The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060003 Odd numbers not of the form p + 2*k^2, k>0, p prime. 7
 1, 3, 17, 137, 227, 977, 1187, 1493, 5777, 5993 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is probably finite. Goldbach conjectured that all odd composites are sum of a prime and twice a square. a(9) = 5777 and a(10) = 5993 are the only known exceptions. Elements a(2) .. a(8) are the odd Stern primes (cf. A042978). The next element of the sequence, if it exists, is larger than 10^9. - M. F. Hasler, Nov 16 2007 The next term, if it exists, is larger than 2 * 10^13. - Benjamin Chaffin, Mar 28 2008 Terms greater than 3 are of the form 6*n-1. - Dan Graham, Mar 03 2015 REFERENCES David Wells, Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, 1997, page 76. LINKS Laurent Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47. Mark VandeWettering, Toying with a lesser known Goldbach Conjecture, 2006. MATHEMATICA Do[ k = 1; While[ n - 2*k^2 > 1 && !PrimeQ[ n - 2*k^2 ], k++ ]; If[ n - 2*k^2 < 0, Print[n] ], { n, 5, 10^8 } ] PROG (PARI) forstep( n=1, 2^30, 2, for(s=1, sqrtint(n\2), if(isprime(n-2*s^2), next(2))); print(n)) \\ M. F. Hasler, Nov 16 2007 CROSSREFS Cf. A042978. Sequence in context: A105630 A199138 A006290 * A350736 A231909 A331688 Adjacent sequences:  A060000 A060001 A060002 * A060004 A060005 A060006 KEYWORD nonn,hard,more AUTHOR Robert G. Wilson v, Mar 14 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 6 12:26 EDT 2022. Contains 355110 sequences. (Running on oeis4.)